A block of weight W is supported by three str | vedclass

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(B) Let the junction point where the three strings meet be in equilibrium.The forces acting at the junction are:$1$. Tension $T_3$ acting vertically d

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$T_1=T_3$

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(B) Let the junction point where the three strings meet be in equilibrium.The forces acting at the junction are:$1$. Tension $T_3$ acting vertically downwards,which must balance the weight $W$,so $T_3 = W$.$2$. Tension $T_1$ acting horizontally to the left.$3$. Tension $T_2$ acting along string $B$ at an angle of $135^{\circ}$ with string $A$.Resolving the forces into horizontal and vertical components:For horizontal equilibrium: $T_2 \cos(180^{\circ} - 135^{\circ}) = T_1 \implies T_2 \cos(45^{\circ}) = T_1 \implies T_2 / \sqrt{2} = T_1$.For vertical equilibrium: $T_2 \sin(180^{\circ} - 135^{\circ}) = T_3 \implies T_2 \sin(45^{\circ}) = T_3 \implies T_2 / \sqrt{2} = T_3$.Comparing the two equations,we get $T_1 = T_2 / \sqrt{2}$ and $T_3 = T_2 / \sqrt{2}$.Therefore,$T_1 = T_3$.

$A$ block of weight $W$ is supported by three strings as shown in the figure. Which of the following relations is true for the tension in the strings? (Here $T_1, T_2,$ and $T_3$ are the tensions in strings $A, B,$ and $C$ respectively.)

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